Cherenkov Ray Cones in Crystalline Media

The rings of light on the photographic plate in Cherenkov emission in crystalline media are shown to come from sections of the Cherenkov `ray cones' rather than the `wave-normal cones'. Equations are derived for the ordinary and extraordinary ray cones emitted by a charge moving in an arbitrary direction in a uniaxial crystal. It is shown that, for a range of angles between the direction of motion of the charge and the optic axis, the ray cones intersect one another, whereas the wave-normal cones do not do so. A method is given to obtain sections of the ray cones on the photographic plate from corresponding sections of the wave-normal cones emitted by a charge moving along a principal axis of a biaxial crystal. It is applied to study the Cherenkov analogue of internal conical refraction that occurs for a critical velocity of the charge such that a Cherenkov-wave normal coincides with a binormal of the crystal.